1. Engineering Analysis ENG 3420 Fall 2009
Dan C. Marinescu
Office: HEC 439 B
Office hours: Tu-Th 11:00-12:00

2. Lecture 20 Last time: Today Next Time The inverse of a matrix
Iterative methods for solving sytems of linear equations
Gauss-Siedel
Jacobi
Today
Relaxation
Non-linear systems
Random variables, probability distributions, Matlab support for random variables.
Next Time
Linear regression
Linear least squares regression
Lecture 20 2

3. Relaxation
To enhance convergence, an iterative program can introduce relaxation where the value at a particular iteration is made up of a combination of the old value and the newly calculated value: where  is a weighting factor that is assigned a value between 0 and 2.
0<<1: underrelaxation
=1: no relaxation
1<≤2: overrelaxation

4. Nonlinear Systems
Nonlinear systems can also be solved using the same strategy as the Gauss-Seidel method - solve each system for one of the unknowns and update each unknown using information from the previous iteration.
This is called successive substitution.

5. Newton-Raphson
Nonlinear systems may also be solved using the Newton-Raphson method for multiple variables.
For a two-variable system, the Taylor series approximation and resulting Newton-Raphson equations are:

7. Probability and statistics concepts
See class notes:
Probability
NASA lecture